intelligent databases / game theory 2003. peter van emde boas intelligent databases game theory part
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Intelligent Databases / Game Theory 2003. Peter van Emde Boas
INTELLIGENT DATABASESGAME THEORY PART 1
PREFACE
Peter van Emde Boas
ILLC-FNWI-UvABronstee.com Software & Services B.V.
2003
See: http://staff.science.uva.nl/~peter/teaching/idb03.html
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
AGENDA
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Games in Computer Science• Evasive Graph properties (1972-74)• Information & Uncertainty (Traub ea. - 1980+)• Pebble Game (Register Allocation, Theory 1970+)• Tiling Game (Reduction Theory - 1973+)• Alternating Computation Model (1977-81)• Interactive Proofs /Arthur Merlin Games (1983+)• Zero Knowledge Protocols (1984+)• Creating Cooperation on the Internet (1999+)• E-commerce (1999+)• Logic and Games (1950+)• Language Games, Argumentation (500 BC)
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Games in Computer Science
• Cryptography Scenario Analysis– Secure Information Transmission– Secure transactions
• Agent Technology• Distributed Computation
– Leader Election– Byzantine Agreement
• Robot Soccer
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
SECURE COMMUNICATION
ALICE BOB
ELIAS
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
SECURE TRANSACTIONS
ALICE
BOB’s BANKALICE’s BANK
BOBCROOKS
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Computer Science for Games
• Analysis Game trees (Checkers, Chess, Backgamon, Go, Othello, ...)
• Theory of - pruning
• Artificial Intelligence
• and (also) Computer Games....
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Previous Ph.D. Research
© Peter van Emde Boas © Peter van Emde Boas
Anette Bleeker:Modal Logic & Cryptographic Protocols
Marc Pauly:Power of Coalitions
© Peter van Emde Boas
Hans van Ditmarsch:Knowledge GamesCluedo Analysis
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Game Theory
• Theory of Strategic Interaction
• Attributes– Discrete vs. Continuous– Cooperative vs. Non-Cooperative– Full Information vs.
Incomplete Information(Knowledge Theory)
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Discrete / Continuous
Combinatorial AnalysisBackward InductionNumber Theory(Conway Guy Berlekamp)
Equilibria theory (Nash)Stochasitic FeaturesOptimization
Other names of importance:Von Neumann & MorgensternAumannShapleyHarsanyi
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
© Games Workshop © Games Workshop
URGAT THORGRIM
Introducing the Opponents
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
STRATEGIC VOTING
Alice Bob
Boris Horace Maurice
Genootschap voor deVerpoldering van de
Cultuur
Prefs Boris Horace Maurice1 Alice Nobody Bob2 Nobody Alice Alice3 Bob Bob Nobody
Agenda:
Proposition: Alice to become Member
Amendment: Bob to replace Alice
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
STRATEGIC VOTING (2)
Boris Horace Maurice
Genootschap voor deVerpoldering van de
Cultuur
Alice Bob
Prefs Boris Horace Maurice1 Alice Nobody Bob2 Nobody Alice Alice3 Bob Bob Nobody
Agenda:
Proposition: Alice to become Member
Amendment: Bob to replace Alice
Procedural Proposal: First Vote on adding a new member at all !!!
1: Horace: Bob Alice in Amendment
2: Maurice: Alice Bob in Amendment
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Auctions
FOR SALE
ALICE HORACE
£ 3M or£ 4M
MAURICE
£ 3M or£ 4M
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Auctions
Dogbert’s advice to Alice:
Run a Second-Price Auction© Scott Adams
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
AuctionsSecond Price Auction Incites Buyers to submit true bids:
Winner: Had I bid something else, it wouldn’t matter forthe price paid, except when I had bid less than myopponent, in which case I would have scored nothing.....
Loser: Had I bid something else, it wouldn’t have madea difference, except when I would have bid more than myopponent, in which case I would have paid more thanwhat I believe the house should cost......
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Expected Gain for AliceHorace’s bid £ 3 M £ 4 M
Maurice’s bid
£ 3 M
£ 4 M
½
½
½ ½
£ 0 M £ 0 M
£ 0 M £ 1 M
Expected profit: ¾ * £ 0 M + ¼ * £ 1 M = £ ¼ M
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
AuctionsDogbert’s advice to Alice:
Run a Second-Price Auction
Ratbert’s advice to Horace and Mauricein case of First-Price Auction:
Use mixed strategy: if willing to pay £ 4Mbid := £ cM with such a distribution thatP( bid ≤ £ bM ) = (b-3) / (4-b)
© Scott Adams
© Scott Adams
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
AUCTION
What Ratbert’s advice amounts to
Alice sells to Horace
Alice sells to Maurice
Maurice’s Bid
£ 3M£ 3M £ 3.5M
£ 4MMaurice’s Reservation Price
£ 4M
£ 3M
£ 3M
£ 3.5M
Horace’s Bid
Horace’s Reservation Price
© Scott Adams
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Ratbert’s AdviceExpected gain for Horace with reservation value £ 4 M
When bidding £ b M:
When Maurice has reservation value £ 3 M : £ (4-b) M (which happens with prob. ½ )When Maurice has reservation value £ 4 M : £ (4-b) M only in case he wins the auction (which happens with prob. ½ (b-3) / (4-b) )
in total: (4-b)* ( ½*(1 + (b-3) / (4-b))) = ½I.E., constant which not depends on b !
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
Ratbert’s AdviceExpected gain Alice:
E(gainA ) = E(gainA | H wins) * P( H wins) + E(gainA | M wins) * P( M wins) =
E(gainA | H wins) =E(gainA | H wins, H:3) * P(H:3) + E(gainA | H wins, H:4) * P(H:4) =
½ * E(gainA | H wins, H:4) =½ * (1 - E(gainH | H wins, H:4) ) = ¼
by symmetry
This is exactly what Alice can expect if she followsDogbert’s advice..... Can she hope to gain more ???
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
PLATFORM SELECTION
Constructing a Platform for the Haran Ghomarist Party
ISSUE In Favour Against
Prohibition of SmokingElimination Mobile PhonesSodomy LawsProposition 3696 year Curriculum in AcademiaPraying in School...........
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
PLATFORM SELECTION (2)
Akalawite Party Hamatite Party
0 1
{ Borg Hive } { Ferengi Alliance }
Intelligent Databases / Game Theory 2003. Peter van Emde Boas
PLATFORM SELECTION (3)
Akalawite Party Hamatite Party
0 1
{ Borg Hive } { Ferengi Alliance }
Ghomarist Party